Planetary Orbits In Binary Systems Research Articles

ON THE HABITABLE ZONES OF CIRCUMBINARY PLANETARY SYSTEMS

The effect of the stellar flux on exoplanetary systems is becoming an increasingly important property as more planets are discovered in the Habitable Zone (HZ). The Kepler mission has recently uncovered circumbinary planets with relatively complex HZs due to the combined flux from the binary host stars. Here we derive HZ boundaries for circumbinary systems and show their dependence on the stellar masses, separation, and time while accounting for binary orbital motion and the orbit of the planet. We include stability regimes for planetary orbits in binary systems with respect to the HZ. These methods are applied to several of the known circumbinary planetary systems such as Kepler-16, 34, 35, and 47. We also quantitatively show the circumstances under which single-star approximations break down for HZ calculations.

Stability of planetary orbits in binary systems

Stability of planetary orbits in binary systems

A Statistical Stability Analysis of Earth‐like Planetary Orbits in Binary Systems

ABSTRACTThis paper explores the stability of an Earth‐like planet orbiting a solar‐mass star in the presence of a stellar companion, using ∼400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a statistical analysis of the ensuing dynamics for ∼500 orbital configurations defined by the following set of orbital parameters: the companion mass MC, the companion eccentricity e, the companion periastron p, and the planet’s inclination angle i relative to the stellar binary plane. Specifically, we generate a large sample of survival times (τs) for each orbital configuration through the numerical integration of N≫1 equivalent experiments (e.g., with the same orbital parameters but randomly selected initial orbital phases). We then construct distributions of survival time using the variable μs≡log τs (where τs is in years) for each orbital configuration. The primary objective of this work is twofold. First, we use the mean of the distributions to gain a better understanding of orbital configurations that, while unstable, have sufficiently long survival times to make them interesting to the study of planet habitability. Second, we calculate the width, skew, and kurtosis of each μs distribution and look for general features that may aid further understanding and numerical exploration of these chaotic systems. To leading order, most distributions are nearly Gaussian, with a width of σ∼0.5, although the longest‐lived systems display substantial (non‐Gaussian) tails. As a result, many independent realizations of these systems must be considered in order to characterize the survival time. The situation is more complicated for orbital configurations with longer mean survival times, owing in part to the increasing importance of resonances.

Stability of planetary orbits in binary systems

Stability of S-type and P-type planetary orbits in binary systems of different mass and separation ratios is inves- tigated. Criteria for stable, marginally stable and unstable planetary orbits are specified. These criteria are used to determine regions of stability of planetary orbits in different binary systems with Jupiter-type planets. The obtained results show that the regions of stability for S-type orbits depend on the distance ratio between the star and planet, and the stellar companions, in the range of 0.22 and 0.46, depending on the mass ratio. For P-type orbits, the regions of stability also depend on that distance ratio, in the range of 1.75 and 2.45, again depending on the the mass ratio. Applications of these results to three observed binary systems with giant planets, namely, τ Boo, HD 195019 and GJ 86, show that the orbits of the giant planets in those systems can be classified as stable, as expected.

Dynamical Stability of Earth‐like Planetary Orbits in Binary Systems

ABSTRACTThis paper explores the stability of an Earth‐like planet orbiting a solar‐mass star in the presence of an outer‐lying intermediate‐mass companion. The overall goal is to estimate the fraction of binary systems that allow Earth‐like planets to remain stable over long timescales. We numerically determine the planet’s ejection time τej over a range of companion masses (MC = 0.001–0.5 M⊙), orbital eccentricities ϵ, and semimajor axes a. This suite of ∼40,000 numerical experiments suggests that the most important variables are the companion’s mass MC and periastron distance Rmin = a(1 - ϵ) to the primary star. At fixed MC, the ejection time is a steeply increasing function of Rmin over the range of parameter space considered here (although the ejection time has a distribution of values for a given Rmin). Most of the integration times are limited to 10 Myr, but a small set of integrations extend to 500 Myr. For each companion mass, we find fitting formulae that approximate the mean ejection time as a function of Rmin. These functions can then be extrapolated to longer timescales. By combining the numerically determined ejection times with the observed distributions of orbital parameters for binary systems, we estimate that (at least) 50% of binaries allow an Earth‐like planet to remain stable over the 4.6 Gyr age of our solar system.

Stability of planetary orbits in binary systems

The possible existence of stable orbits is investigated in binary systems using Hill's method. Analytical stability conditions are established for satellites, for inner planets and for outer planets, allowing arbitrary values for the mass-ratio of the binary.